His resume certainly is not reasonable. He wrote an awful book called "The Skeptical Environmentalist" in which he was caught using cherry picking and other faulty statistical techniques to make the case that world environmental problems were exaggerated. The Danish Committee on Scientific Dishonesty investigated charges againstt, and decided the book itself was scientifically dishonest, but acquitted Lomborg of deliberate dishonesty on grounds that the lacked scientific training, and therefore his he may have made honest errors rather that being deliberately dishonest .
The things the society found wrong with his book included:
1. Fabrication of data;
2. Selective discarding of unwanted results (selective citation);
3. Deliberately misleading use of statistical methods;
4. Distorted interpretation of conclusions;
5. Plagiarism;
6. Deliberate misinterpretation of others' results.
Haven't read the new book, but Joe Romm (who I respect on scientific and technical issues even though we have some strong disagreements on political economy) does not think highly of it:
http://gristmill.grist.org/story/2007/9/13/105130/672
http://gristmill.grist.org/story/2007/9/14/142514/357
http://gristmill.grist.org/story/2007/9/17/151133/245